Combining Wave Energy with Wind and Solar: Short-Term Forecasting

Renewable Energy 81 (2015) 442e456

Contents lists available at ScienceDirect

Renewable Energy

journal homepage: www.elsevier.com/locate/renene

Combining wave energy with wind and solar: Short-term forecasting

* Gordon Reikard a, , Bryson Robertson b, Jean-Raymond Bidlot c

® a Statistics Department, U.S. Cellular , USA b University of Victoria, Canada c European Center for Medium-Range Weather Forecasts, UK article info abstract

Article history: While wind and solar have been the leading sources of renewable energy up to now, waves are Received 13 December 2014 increasingly being recognized as a viable source of power for coastal regions. This study analyzes inte- Accepted 12 March 2015 grating wave energy into the grid, in conjunction with wind and solar. The Pacific Northwest in the Available online United States has a favorable mix of all three sources. Load and wind power series are obtained from government databases. Solar power is calculated from 12 sites over five states. Wave energy is calculated Keywords: using buoy data, simulations of the ECMWF model, and power matrices for three types of wave energy Wave energy converters. At the short horizons required for planning, the properties of the load and renewable energy Wind power Solar power are dissimilar. The load exhibits cycles at 24 h and seven days, seasonality and long-term trending. Solar Forecasting power is dominated by the diurnal cycle and by seasonality, but also exhibits nonlinear variability due to Grid integration cloud cover, atmospheric turbidity and precipitation. Wind power is dominated by large ramp events eirregular transitions between states of high and low power. Wave energy exhibits seasonal cycles and is generally smoother, although there are still some large transitions, particularly during winter months. Forecasting experiments are run over horizons of 1e4 h for the load and all three types of renewable energy. Waves are found to be more predictable than wind and solar. The forecast error at 1 h for the simulated wave farms is in the range of 5e7 percent, while the forecast errors for solar and wind are 17 and 22 percent. Geographic dispersal increases forecast accuracy. At the 1 h horizon, the forecast error for large-scale wave farms is 39e49 percent lower than at individual buoys. Grid integration costs are quantified by calculating balancing reserves. Waves show the lowest reserve costs, less than half wind and solar. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction The Paciﬁc Northwest in the United States has a favorable mix of all three sources, as well as robust data sets. Load and wind power While wind and solar have been the leading sources of renew- are published by the Bonneville Power Administration (BPA). able energy up to now, waves are increasingly being recognized as a Operating as a wholly-owned subsidiary of the U.S. Department of viable source of power for coastal regions [1,2]. One of the major Energy, BPA's service territory includes Idaho, Oregon, Washington, issues in integrating renewable energy into the grid is short-term and parts of Montana, California, Nevada, Utah and Wyoming. The forecasting. In the electric power industry, forecasts are used in bulk of BPA's generating capacity is hydroelectric, but as of 2013, operational planning, peak load matching, switching sources and some 4515 megawatts (MW) of wind capacity had been installed, planning for reserve usage, i.e., buffering against the uncertainty with an additional 2500 MW planned for 2015 [3]. caused by deviations between supply and demand, and deviations Solar power development has been less extensive, but plans are between supply and forecasts. The horizons range from as little as a underway to install capacity in inland areas that have less precip- few minutes to several hours, but are typically short. This study itation and more continuous sunlight. Data sets for 25 solar sta- analyzes integrating wave energy into the power grid, in conjunc- tions, over ﬁve states, are publically available from the University of tion with wind and solar. The goal is to quantify the relative costs Oregon's solar radiation measurement laboratory [4]. associated with all three types of renewable energy. The wave energy on the outer continental shelf off the coasts of Washington and Oregon has been estimated at 179 terawatts (TW)

* Corresponding author. Tel.: þ1 773 399 8802. in deep water and 140 TW closer to the coast, although it is likely E-mail address: [email protected] (G. Reikard). that only a fraction of this can be extracted [5]. A more realistic http://dx.doi.org/10.1016/j.renene.2015.03.032 0960-1481/© 2015 Elsevier Ltd. All rights reserved. G. Reikard et al. / Renewable Energy 81 (2015) 442e456 443 number for the wave energy that could be generated with existing significant wave height (HSt), in meters, and the mean wave period technologies is on the order of 500 MW. Data on the wave height (TMt), in seconds. Fig. 3 shows the buoy locations. Figs. 5e6 show and period is available for several buoy sites from the National Data the wave height and period at Cape Elizabeth. Missing values were Buoy Center, operated by the National Oceanographic and Atmo- interpolated using ECMWF model simulations. spheric Administration [6]. Wave parameters over wider areas are The ECMWF wave model is a third-generation physics-based simulated using the European Center for Medium-range Weather model [7]. Large-scale physics-based wave models have been in Forecasts model (ECMWF, 2015). operation since the 1960s, and have been updated repeatedly since The organization of this study is as follows. Section 2 reviews this time [8e12]. The ECMWF wave and atmospheric models have the load, solar and wind data. The calculations for wave energy are been coupled since June 1998. In third-generation models of this presented in Section 3. The forecasting methodology is set out in type, the major properties of the wave spectra are determined by Section 4. Forecasting tests and grid integration experiments are the action balance equation. Let N denote the wave action density, run in Sections 5e6. Section 7 concludes. equal to the energy density divided by the intrinsic frequency. Let t denote time, and x, y denote distance in the Cartesian coordinates. 2. The load, wind and solar power Let s denote the intrinsic frequency and g denote the wave propagation direction. Let Cg denote the wave action propagation speed The database was compiled for January 1, 2012 through in (x, y, s, g) space, and S denote the combined source and sink December 31, 2013, at an hourly resolution. The load, wind and terms. In deep water, the three major components of S are the input solar data were converted to hourly from the original 5 min and by wind (SIN), nonlinear waveewave interactions (SNL) and wave 15 min values. Table 1 gives the sources. dissipation through white-capping (SWC). The action balance Fig. 1 shows the load over the three month period Januar- equation can be expressed in the following form: yeMarch 2012. The load exhibits cycles at 24 h and 7 days, seasonal cycles at 12 months, and a long-term trend associated with the vN=vt þ vCg;xN vx þ vCg;yN vy þ vCg;sN vs þ vCggN vg ¼ S; growth of the economy. The seasonal cycle peaks during the winter S ¼½ðSINÞþðSNLÞþðSWCÞ months. The amplitude of the 7-day cycles varies from week to (1) week. There are occasional outliers, generally associated with weather events. Since January 2010, the average resolution of the grids simulated BPA's wind generating capacity currently includes 43 sites, with by the wave model has been 28 square km. Hourly data from the several more under development. Maps of operational and planned short range forecasts were obtained from the ECMWF archive to installations are available at the BPA website [3]. The majority have produce continuous time series at the four buoy locations. Model been located in the Columbia River gorge, with additional stations fields were interpolated from the original grid to the buoy co- along the Oregon coast and further inland. The average wind power ordinates using a bilinear method. The simulated parameters were in 2013 was 1218 MW, or 27 percent of capacity. Fig. 2 shows the the significant wave height and the zero-crossing mean wave wind power series over the same three month interval. The most period, which shows the closest correlation with the mean wave prominent feature in wind is large ramp eventseirregular transi- period from the buoy data. tions between states of high and low power. In most prior studies, the wave energy has been calculated using Of the 25 solar data sets, many had extensive missing values. the flux. Letting g denote the acceleration caused by gravity 3 Twelve sites which had complete observational records were used. (9.8086 m/s/s), and r denote the density of seawater (1025 kg/m ), These include six in Oregon, three in Idaho, and one each in the flux (in kW/m) is given by: Montana, Utah and Wyoming (see Table 1). Fig. 3 shows the loca- h . i tions on a map. The values for ground level irradiance are the global ¼ 2r 2 z : 2 EFt g 64p HStTMt 0 491 HStTMt (2) horizontal component, in watts per meter squared (W/m2). All the generation is assumed photovoltaic, so that the power can be Some recent studies have proposed simulating a generic con- calculated as a ratio to irradiance. The ratio was set to 7.2 percent. verter in which the power is proportional to the flux for lower Irradiance reaching the ground is intermittent, due to the effects values of the wave height, but levels off above a given threshold of cloud cover, atmospheric turbidity and precipitation. However, [13]. The procedure used here, however, is to calculate the power some of this variability can be mitigated by dispersing sites over flow from three types of wave energy converters (WECs), an wide areas. The power calculations were run for the individual attenuator, a point absorber, and an oscillating device. There is an sites, then aggregated and scaled up to simulate 500 MW of solar important difference between these and the generic converter: the power. Fig. 4 shows the combined solar power series. There is a wave energy is a nonlinear function of the wave height and period, strong seasonal cycle in the solar data, which runs counter to the rather than the wave height squared, typically rising in proportion seasonal cycle in the load: solar power peaks during the summer to both parameters and then declining as a function of the period months. The main feature at short horizons is the diurnal cycle. [14]. While the aggregate series is much smoother than the data at in- The Pelamis P2 device is an offshore converter, operating in dividual sites, there is still evidence of nonlinear variability: the depths greater than 50 m [15e18]. The machine consists of a series amplitude of the cycle can change from day to day, while weather of semi-submerged cylindrical sections linked by hinged joints. events can result is large changes in power over intervals of a few The wave-induced motion causes hydraulic cylinders to pump hours. high pressure oil through motors driving electrical generators. The Pelamis conversion matrix is given in Fig. 7. The maximum power 3. Calculating wave power generated by the converter is 750 kW, at wave heights greater than or equal to 5.5 m. The resolution of the matrix is 0.5 m for the The primary source for the wave data is four buoys off the coasts wave height and 0.5 s for the wave period. The matrix was of Washington and OregoneCape Elizabeth, the Columbia River Bar, increased to a resolution of 0.1 m for the wave height, using linear Stonewall Banks and Umpqua. Table 1 provides the buoy identifiers, interpolations. the latitude and longitude, the depth, the resolution, and the Performance matrices for several other WECs have recently number of usable values. The buoy data sets all include the been published [19]. The floating heave buoy array is composed of Table 1 The data.

Database and variables Units Location Resolution Elevation or depth, usable values

All data is for the period January 1, 2012 through December 31, 2013.

1] The load Power load Megawatts BPA service area 5 min Source: Bonneville Power Administration (BPA) website (http://transmission.bpa.gov/Business/Operations/Wind/).

2] Wind power Megawatts 43 wind farms 5 min Source: Bonneville Power Administration (BPA) website (http://transmission.bpa.gov/Business/Operations/Wind/).

3] Solar Ashland, OR Watts/m2 42.19 N, 122.71 W 15 min Elevation: 595 m Burns, OR Watts/m2 43.52 N, 119.02 W 15 min Elevation: 1295 m Challis, ID Watts/m2 44.45 N, 114.31 W 15 min Elevation: 1651 m Dillon, MT Watts/m2 45.21 N, 112.62 W 15 min Elevation: 1590 m Eugene, OR (two series) Watts/m2 44.05 N, 123.07 W 15 min Elevation: 150 m Green River, WY Watts/m2 41.46 N, 109.44 W 15 min Elevation: 1000 m Hermiston, OR Watts/m2 45.82 N, 119.28 W 15 min Elevation: 180 m Moab, UT Watts/m2 38.58 N, 109.54 W 15 min Elevation: 1000 m Picabo, ID Watts/m2 43.31 N, 114.17 W 15 min Elevation: 1472 m Silver Lake, OR Watts/m2 43.31 N, 121.06 W 15 min Elevation: 1355 m Twin Falls, ID Watts/m2 42.55 N, 114.35 W 15 min Elevation: 1200 m Source: University of Oregon's solar radiation measurement laboratory (http://solardata.uoregon.edu).

4] Waves NDBC 46041, Cape Elizabeth Wave height, meters 47.35 N, 124.73 W Hourly Depth: 114.3 m Wave period, seconds Usable values: 17,241 NDBC 46029, Columbia River bar Wave height, meters 46.14 N, 124.51 W Hourly Depth: 135.3 m Wave period, seconds Usable values: 10,941 NDBC 46050, Stonewall Banks Wave height, meters 44.64 N, 124.53 W Hourly Depth: 128.1 m Wave period, seconds Usable values: 17,491 NDBC 46229, Umpqua Wave height, meters 43.77 N, 124.55 W 30 min Depth: 187.1 m Wave period, seconds Usable values: 17,126 Waves: National Data Buoy Center: www.ndbc.noaa.gov several heaving buoys connected to a submerged reference struc- In this study, one converter is assumed to be located at the buoy ture via a hydraulic system, which generates the electricity. In the site, so that the actual data can be used. The other converters are conversion matrix (Fig. 8), the number of buoys was limited to ten, assumed to be deployed in a line and spaced roughly 150 m apart, yielding a maximum power of slightly over 3600 kW. The floating so that there are 34 converters for every 5 km interval. The data sets three-body oscillating flap device consists of hinged flaps, which for the locations other than the buoy are calculated by overlaying are all connected to a common frame. The matrix is given in Fig. 9. noise processes on the ECMWF model simulations. To estimate the The maximum power is 1665 kW. noise process at the buoy site, the wave height and period data A second issue in wave farm simulation is geographic dispersal. were smoothed using a centered 6 h moving average. The Wave buoy data is known to show a great deal of localized noise. smoothed series were then subtracted from the actual data. The Recent papers have determined that the variance is substantially wave height noise exhibits strong evidence of seasonality: the tails reduced when multiple converters are placed in the same area [20]. are much thicker during the winter than during the summer. The

Fig. 1. The load, Bonneville Power Administration. Left scale: MW. January 1, 2012 to March 31, 2012. G. Reikard et al. / Renewable Energy 81 (2015) 442e456 445

Fig. 2. Wind power, Bonneville Power Administration. Left scale: MW. January 1, 2012 to March 31, 2012. wave period noise is less seasonal, although there are more outliers two noise series were then combined using seasonal weights. The than in the standard normal. distribution with 29 degrees of freedom also worked well for the Preliminary experiments for the wave noise were run using wave period noise. Figs. 10e11 show simulated significant wave draws from various probability distributions. No single distribu- height and period series for Cape Elizabeth. Comparing these with tion replicates the observed pattern in the wave height noise. the buoy data (Figs. 5e6), confirms that they have similar Instead, the preferred procedure was a blend of two distributions, properties. with heavier tails for the winter months. The noise processes that Finally, to create the wave farm simulations, the buoy data most closely approximated the winter wave height were draws and the simulated HSt and TMt series were multiplied by the from a Student-t distribution with 5 degrees of freedom. The wave coefficients in the converter matrices. The main forecasting tests height during the summer months also shows somewhat heavier below are run for the 5 km wave farms, i.e., 34 converters. tails than in the Gaussian normal. A student-t distribution with 29 However, in the grid integration tests, larger wave farms had to degrees of freedom closely replicated the observed values. The be simulated. These were calculated by simulating additional

Fig. 3. The buoys and the solar stations. Triangles: wave buoys. Squares: solar sites. 446 G. Reikard et al. / Renewable Energy 81 (2015) 442e456

Fig. 4. Simulated solar power, 12 sites. Left scale: MW. January 1, 2012 to January 31, 2012. converters over wider areas, and combining the power series of lower power. The series for the oscillating flap device is less at all four sites. To facilitate comparison, all the large wave volatile than the heave buoy array but still shows irregular sharp farms were normalized to an average hourly power output of peaks, as well as fluctuations between states of low and interme- 500 MW. diate power. Figs. 12e14 show the power series from the larger wave farms for the Pelamis, the heave buoy array and oscillating flap device. 4. Forecasting methodologies There are some visible differences between the simulated series. The Pelamis power series exhibits repeated transitions between One issue that has arisen repeatedly in the wave literature is the states of high and low power, although within a narrower range choice of physics-based versus time series models. Physics models than the other two converters. Even during the winter months, the have been found to have good forecasting properties over longer power rarely exceeds 1900 MW. By comparison, the power series horizons for waves [21e25]. However, over short horizons, time from the heave buoy array is considerably more volatile, with series models have often proven to be more accurate. Comparisons intermittent large spikes, and greater variability even during states of physics and statistical methods have found that the convergence

Fig. 5. Signiﬁcant wave height, Cape Elizabeth. Left scale: Meters. January 1, 2012 to March 31, 2012. G. Reikard et al. / Renewable Energy 81 (2015) 442e456 447

Fig. 6. Mean wave period, Cape Elizabeth. Left scale: seconds. January 1, 2012 to March 31, 2012. point for waves, i.e., the horizon at which the two methods achieve the power production forecasts for all three types of renewable comparable degrees of accuracy, is about 6 h [26,27]. For solar, the energy were run using time series models. convergence time is probably shorter, on the order of 2 h [28,29]. The basic model used here is regression with stochastic co- The evidence on wind is limited, but time series models have efﬁcients. Models of this type can capture a great deal of nonlinear generally been preferred at short intervals [30,31]. Consequently, variability [32,33]. Let Yt denote a time series, let the resolution be

Fig. 7. Conversion matrix for the Pelamis P2 device. Power is in kilowatts.

Fig. 8. Conversion matrix for the ﬂoating heave buoy array. Power is in kilowatts. 448 G. Reikard et al. / Renewable Energy 81 (2015) 442e456

Fig. 9. Conversion matrix for the ﬂoating three-body oscillating ﬂap device. Power is in kilowatts.

1 h, let u denominate a coefficient, and let the subscript t denote time-varying. The inputs to the neural net were the same as in the time variation. The model is of the form: regressions. When the data incorporate cycles at regular frequencies, as is the case with the load and solar power, ARIMA-type models have lnY ¼u þ u lnY þ u lnY þ u lnY t 0t 1t t 1 2t t 2 3t t 3 been found to be more effective than regressions on levels. 2 (3) Following the notation of Box and Jenkins [44], let f(L) be the þ u lnY þ εt; εt P 0; y 4t t 4 t autoregressive operator, represented as a polynomial in the lag ¼ e … p 2 operator (L): f(L) 1 f1L fpL . Let F(L) be the seasonal where P is the probability distribution and yt is the residual vari- autoregressive operator. Let q(L) be the moving average operator: ance. Additional lags can be used as needed, but the Akaike infor- q q(L) ¼ 1 þ q1L þ … þ qqL , and Q(L) be the seasonal moving average mation criterion favored limiting the lags to 4 h [34]. There was operator. Let the superscript x denote the order of differencing, and little evidence of any diurnal cycle in the wave data. the superscript z denote the order of cyclical differencing. Let the Neural networks have often been the preferred forecasting superscript f denote the cyclical frequency. For hourly data, f ¼ 24. fi method for scienti c time series. There is a vast literature on using The model is then of the form: neural networks to predict renewable energy [35e43]. The system architecture used here consists of a multilayer perceptron, trained z ð Þx f ¼½ ð ÞQ ð Þ= ð Þ ð Þε using a backpropagation algorithm. For the time series analyzed 1 L 1 L lnYt qt L t L ft L Ft L t (4) below, the net was specified with three hidden layers, and one direct connection. It was trained by epoch, i.e., a forward and backward pass through all observations in the sample, rather than The coefficients are again time-varying. by example, i.e., a pass over individual observations. The input and The forecasting experiments are set up as follows. The first 500 bias weights were not retained from the previous period, but rather observations are used as a training sample. The power series are were restarted at each time point, so that in effect the weights are then forecasted iteratively. In each instance, the models are

Fig. 10. Simulated signiﬁcant wave height series, Cape Elizabeth. Left scale: Meters. January 1, 2012 to March 31, 2012. G. Reikard et al. / Renewable Energy 81 (2015) 442e456 449

Fig. 11. Simulated mean wave period series, Cape Elizabeth. Left scale: seconds. January 1, 2012 to March 31, 2012. estimated over prior values, forecasted, then re-estimated over the 5. Forecasting tests: initial findings most recent value, etc. All the predictions are true out-of-sample forecasts, in that they use only data prior to the start of the fore- Table 2 presents the forecast error for the three types of cast horizon. All the intervening periods are omitted. In other words, renewable energy, the load and the net power, i.e., the load less the for horizon t þ 2, the forecasts for t þ 1 are excluded. The measure of supply from wind, waves and solar. The tests are run for horizons of forecast accuracy reported is the mean absolute percent error. 1e4 h, although the main interest is the 1 h horizon. Table 3 reports Time-varying parameter regressions can be estimated either the estimated coefficients. using a Kalman filter [45] or a moving window. With an unre- fi fi stricted Kalman lter, the coef cients behave as a random walk. 5.1. Waves This was found to impart too much volatility to the forecast values, reducing predictive accuracy. The choice is therefore between The model is a regression on lags (Equation (3)). The neural fi imposing restrictions on the lter, or varying the width of the network was also used for waves, but the results were extremely moving window [46]. Several preliminary experiments were run. In similar, so only the regression is reported. The forecasts were run most of the tests below, a width of 480 h is used. both for the individual buoys, the 5 km wave farms, and the larger

Fig. 12. Large wave farm simulation, Pelamis. Left scale: MW. January 1, 2012 to March 31, 2012. 450 G. Reikard et al. / Renewable Energy 81 (2015) 442e456

Fig. 13. Large wave farm simulation, heave buoy array. Left scale: MW. January 1, 2012 to March 31, 2012.

500 MW wave farms combining all four sites, for each type of farm than at the buoy, and 40 percent lower at the large wave device. farm. At Cape Elizabeth, the errors for the 5 km wave farm at the 1 h The results for the heave buoy array show an even larger pro- horizon range from 6.5 to 8.7 percent. At the Columbia River Bar, portional improvement. The errors for the individual buoys average they range from 6.2 to 8.3 percent. At Stonewall Banks, they range 11.08 percent. This declines to 6.3 percent at the 5 km wave farms, from 6.2 to 8.5 percent. At Umpqua, they range from 6.3 to 8.6 an improvement of 43 percent, and 5.2 percent at the combined percent. The heave buoy array shows the smallest errors, while the wave farm, a reduction in the forecast error of 49 percent. errors for the Pelamis and the oscillating ﬂap device are usually The oscillating ﬂap device shows an average error of 11.44 fairly similar. percent for the individual buoys, and 8.54 percent for the 5 km Averaging the four sites, the Pelamis shows errors of 10.2 wave farms, a proportional improvement of 25 percent. The error percent for the individual buoys. This falls to 7.8 percent for the for the combined wave farm is 6.95 percent, or 39 percent lower 5 km wave farms, and 5.9 percent when the four sites are com- than at the individual buoy sites. bined. The forecast error is 23 percent lower at the 5 km wave As the horizon extends, the forecast errors increase, but the effects of geographic dispersal are still substantial. At 4 h, the

Fig. 14. Large wave farm power simulation, oscillating flap device. Left scale: MW. January 1, 2012 to March 31, 2012. G. Reikard et al. / Renewable Energy 81 (2015) 442e456 451 improvement in accuracy from the 5 km wave farms relative to the best model for the wind power series shows an error of 22 percent. buoys is 28 percent for the Pelamis, 29 percent for the heave buoy Forecast accuracy deteriorates sharply as the horizon extends. By array, and 22 percent for the oscillating flap device. The improve- 4 h, the wind error has increased to 76 percent. ment from the combined wave farm relative to the buoys is 45 percent for the Pelamis, 43 percent for the heave buoy array, and 38 5.3. Solar percent for the oscillating flap device. There is an extensive literature on forecasting solar power using 5.2. Wind time series models [49,50]. The preferred method for this data set is an ARIMA (3,0,0) (2,1,0), i.e., three proximate lags, differencing at The model for wind is also a regression, on three lags. Several 24 h, and five lags corresponding to the 24 h cycle. As with waves, other methods were also tried, including neural network and state the forecast errors are reported both for the individual sites and for transition models [47,48]. However, these failed to generate any all sites combined. The errors are for daylight hours only; nighttime improvement in accuracy with this data set. At the 1 h horizon, the hours are excluded. At the individual sites, the errors range from a

Table 2 The forecast errors. Figures are the mean absolute percent error.

Variable 1h 2h 3h 4h

Waves Cape Elizabeth, 5 km wave farm, Pelamis 8.32 10.78 14.42 16.05 Cape Elizabeth, 5 km wave farm, heave buoy array 6.54 8.77 11.28 13.98 Cape Elizabeth, 5 km wave farm, oscillating ﬂap device 8.74 11.76 14.93 17.31 Cape Elizabeth, buoy, Pelamis 12.01 15.19 18.44 21.59 Cape Elizabeth, buoy, heave buoy array 10.92 13.62 16.21 18.75 Cape Elizabeth, buoy, oscillating ﬂap device 12.95 16.11 18.33 22.19

Columbia, 5 km wave farm, Pelamis 6.64 8.61 11.68 12.67 Columbia, 5 km wave farm, heave buoy array 6.23 8.44 11.61 12.81 Columbia, 5 km wave farm, oscillating ﬂap device 8.32 11.38 14.24 16.95 Columbia, buoy, Pelamis 10.18 13.49 16.58 19.41 Columbia, buoy, heave buoy array 9.62 12.27 14.64 16.88 Columbia, buoy, oscillating ﬂap device 11.51 14.88 17.91 20.66

Stonewall, 5 km wave farm, Pelamis 8.16 10.62 13.21 15.75 Stonewall, 5 km wave farm, heave buoy array 6.22 8.43 10.69 12.78 Stonewall, 5 km wave farm, oscillating ﬂap device 8.49 11.27 14.08 16.72 Stonewall, buoy, Pelamis 12.85 15.86 18.96 21.89 Stonewall, buoy, heave buoy array 11.76 14.29 16.93 19.34 Stonewall, buoy, oscillating ﬂap device 13.23 16.14 19.11 21.93

Umpqua, 5 km wave farm, Pelamis 8.19 10.53 13.06 15.84 Umpqua, 5 km wave farm, heave buoy array 6.31 8.45 10.13 12.74 Umpqua, 5 km wave farm, oscillating ﬂap device 8.61 11.36 14.14 16.91 Umpqua, buoy, Pelamis 12.91 15.75 18.81 21.71 Umpqua, buoy, heave buoy array 12.04 14.65 17.15 19.58 Umpqua, buoy, oscillating ﬂap device 14.06 17.11 19.98 22.67

Four sites combined, 500 MW wave farm, Pelamis 5.86 7.65 9.56 11.54 Four sites combined, 500 MW wave farm, heave buoy array 5.18 6.72 8.49 10.72 Four sites combined, 500 MW wave farm, oscillating ﬂap device 6.95 9.01 11.21 13.42

Wind BPA Wind power series 22.09 42.16 58.13 77.25

Solar Ashland, OR 63.35 83.56 100.83 102.45 Burns, OR 65.83 87.78 106.34 108.92 Challis, ID 51.27 65.77 81.78 85.19 Dillon, MT 53.54 71.72 77.65 78.36 Eugene, OR 49.91 68.51 73.38 74.29 Eugene, OR (second series) 52.11 82.35 111.64 113.52 Green River, WY 62.58 85.24 89.85 91.82 Hermiston, OR 60.15 86.57 115.36 116.12 Moab, UT 58.27 72.04 86.45 88.21 Picabo, IA 46.52 62.86 70.19 71.79 Silver Lake, OR 61.94 78.06 84.57 89.91 Twin Falls, ID 44.01 56.75 61.48 63.59 All solar sites combined 16.98 23.15 30.20 31.35

Power load and net power Load 0.95 1.72 2.32 2.73 Net power (load less wind) 2.85 7.41 9.35 10.78 Net power (load less solar) 1.88 2.96 3.79 4.39 Net power (load less waves) Pelamis 1.21 2.06 2.74 3.26 Heave buoy array 1.36 2.24 2.96 3.47 Oscillating ﬂap device 1.29 2.18 2.91 3.45

Notes: All series denominated in MW. The forecasts at 1e4 h horizons are run using data at a 1 h resolution. All calculations for solar, including net power, are for daylight hours only. All other calculations are for all time points. 452 G. Reikard et al. / Renewable Energy 81 (2015) 442e456

Table 3 The model coefficients. Figures are regression coefficients. All coefficients are statistically significant at the 1 percent level or better.

RHS variable Aggregate load Solar Wind Waves (Pelamis) Waves (heave buoy array) Waves (oscillating ﬂap device)

Constant ee0.19 0.04 0.05 0.05 Lag, 1 h 1.45 0.98 1.43 0.84 0.85 0.82 Lag, 2 h 0.61 0.04 0.54 0.33 0.29 0.31 Lag, 3 h 0.11 0.07 0.13 0.20 0.01 0.02 Lag, 4 h ee0.05 0.31 0.19 0.18 Lag, 24 h 0.54 0.52 ee e e Lag, 48 h 0.49 0.45 ee e e Lag, 72 h 0.39 eee e e Lag, 96 h 0.34 eee e e Lag, 120 h 0.29 eee e e

R-bar-square 0.991 0.994 0.963 0.989 0.987 0.995

Notes: the models for the load, wind and waves are run on natural logarithms, the model for solar is run on levels. The equations for the aggregate load and the solar power simulation are speciﬁed as ARIMA (5,0,0) (2,1,0) and ARIMA (3,0,0) (2,1,0), i.e., a regression on ﬁve or three proximate lags and two cyclical lags, in 24 h differences. The models for wind and waves are regressions on levels.

Fig. 15. The load forecast error. Left scale: MW. Forecast horizon: 1 h. January 1,2013 to March 31,2013.

Fig. 16. The wind power forecast error. Left scale: MW Forecast horizon: 1 h. January 1, 2013 to March 31, 2013. G. Reikard et al. / Renewable Energy 81 (2015) 442e456 453

Fig. 17. The solar power forecast error. Left scale: MW. Forecast horizon: 1 h. January 1, 2013 to March 31, 2013. minimum of 44 to a maximum of 72 percent at 1 h. The error in- falls sharply during periods of high wind speed, when wind power creases sharply over 2e3 h, but then begins to level off around 4 h. approaches 40 percent of the load, but can rise just as rapidly when Geographic dispersal does achieve a substantial improvement in the wind dies down. predictability. The error for all the sites combined is 17 percent, The net power errors associated with solar and waves are much increasing to 30.2 at 3 h and 31.3 percent at 4 h. smaller. However, these values are not strictly comparable to wind due to differences in scale (at 500 MW each, the mean wave and 5.4. Load and net power solar energy are less than half the mean wind energy of 1218 MW). The net power error for solar is 1.88 percent at 1 h and 4.39 percent The load is forecasted using a two-stage model. The first is an at 4 h. For the three large wave farms, the net power errors are 1.21 ARIMA (3,0,0) (5,1,0), i.e., three proximate lags and lags over five for the Pelamis, 1.36 percent for the heave buoy array and 1.29 24 h intervals. In the second stage, the ARIMA forecast is used as an percent for the oscillating flap device. These increase to 3.24, 3.37 input in a neural network [51]. The forecast error for the load is very and 3.45 percent at 4 h. small, 0.95 percent at 1 h, rising to 2.73 percent at 4 h. While the mean absolute percent error is a widely-accepted The forecasts for the net power use separate equations for the gauge of model accuracy, the distribution of the error is also of in- load and the renewable energy series. The net power associated terest. Figs. 15e20 present the errors for the load, wind, solar and with wind is substantially less predictable than the load: the error waves, over a period of three months. The equation for the load at 1 h is 2.85 percent, rising to over 10 percent at 4 h. The net power tracks quite closely, with the error usually lower than 100 MW, and

Fig. 18. The wave power forecast error, Pelamis. Left scale: MW. Forecast horizon: 1 h. January 1, 2013 to March 31, 2013. 454 G. Reikard et al. / Renewable Energy 81 (2015) 442e456

Fig. 19. The wave power forecast error, heave buoy array. Left scale: MW. Forecast horizon: 1 h. January 1, 2013 to March 31, 2013. rarely exceeding 200 MW (2e3 percent of the load during the same next, while balancing reserves cover imbalances between forecast interval). The wind forecast error shows much greater intermit- and supply at the 1 h horizon, with a 99.5 percent reliability tency. The model alternates between periods of high accuracy and requirement [3]. Capacity-up reserves are reserves associated with periods in which it goes seriously off, with errors in the range of adeﬁcit of energy relative to forecast. Capacity-down reserves are several hundred MW. The solar power error also shows some reserves associated with a surplus. The Federal Energy Regulatory intermittency, although it is considerably smaller than the wind Center (FERC) has also mandated 15 min transmission scheduling error. The most interesting results are for waves, where the error is to assist in integrating variable sources [52]. Unfortunately, wave strongly seasonal. The wave error alternates among two main states. data is not available at the 15 min resolution. Consequently, the During the summer, the error is quite small. During the winter, the reserve calculations were run for the 1 h horizon. average error is higher, with occasional extreme outliers. Table 4 shows the reserves associated with the load, and each of the renewable energy sources, for the overall period, 6. Reserve calculations January 1, 2012 through December 31, 2013. However, reserves are not independent of scale, so the values are also expressed as a At BPA, there are three types of reserves. Regulation reserves percent of power. For capacity down reserves, normally cover differences between the supply and load within 10 min in- expressed as a negative number, the ratio is calculated using the tervals, following reserves apply from one 10 min period to the absolute value.

Fig. 20. The wave power forecast error, oscillating ﬂap device. Left scale: MW. Forecast horizon: 1 h. January 1, 2013 to March 31, 2013. G. Reikard et al. / Renewable Energy 81 (2015) 442e456 455

Table 4 Balancing reserves. Statistics are the mean absolute value of reserves, and reserves as a percent of power.

Site and converter Capacity up Capacity down

Reserves (MW) Reserves % of Power Reserves (MW) Reserves/Power Reserves % of Power

Aggregate load 58.98 0.93 58.89 0.99 Wind (44 sites) 161.24 16.3 94.54 37.1 Solar (12 sites) 67.06 15.2 67.14 15.7 Waves (four sites) Pelamis 28.67 5.6 25.32 5.9 Heaving converter 30.96 4.9 26.63 5.2 Oscillating ﬂap device 35.57 6.5 31.67 7.3

Notes: average wind power is 1218 MW. Average solar and wave power is 500 MW.

For the aggregate load, both capacity-up and capacity-down re- References serves average 59 MW, or slightly less than 1 percent of the power. For wind, capacity-up reserves are as high as 161 MW, or 16 [1] Arinaga RA, Cheung KF. Atlas of global wave energy from 10 years of rean- alysis and hindcast data. Renew Energy 2012;39:49e64. percent of power, while capacity-down reserves are estimated [2] Esteban M, Leary D. Current developments and future prospects of off shore at 94 MW, or 37 percent of power. The asymmetry in the numbers wind and ocean energy. Appl Energy 2011;90:128e36. and the ratios e higher reserves, lower ratios to power – is [3] Bonneville Power Administration, 2015. Website: www.bpa.gov. Wind and load data are available at: http://transmission.bpa.gov/Business/ explained by the fact that surpluses occur primarily during periods Operations/Wind/ Maps of the wind farms are available at: http://www.bpa. of low wind power, typically when wind is ramping up, while gov/transmission/Projects/wind-projects/Documents/bpa-wind-map.pdf deficits occur more often during periods of high wind power, when and at http://www.bpa.gov/transmission/Projects/wind-projects/Pages/ wind power is ramping down. default.aspx. [4] University of Oregon, Solar Radiation Laboratory, 2015. http://solardata. For solar, both capacity-up reserves and capacity-down reserves uoregon.edu. are in the range of 67 MW. Both values are in the range of 15e67 [5] Electric Power Research Institute (EPRI). Mapping and assessment of the percent of power, comparable to capacity-up reserves for wind. United States ocean wave energy resource. 2011 Technical Report. 2011. [6] National Data Buoy Center, 2015. www.ndbc.noaa.gov. For waves, capacity-up reserves range from as little as 28.7 MW [7] European Center for Medium-range Weather Forecasts, 2015. www.ecmwf.int for the Pelamis to 31 MW for the heaving converter and 36 MW for The wave model is available at: http://www.ecmwf.int/en/research/ the oscillating flap device. Expressed as ratios to power, these modelling-and-prediction/marine. [8] Hasselmann K, Ross DB, Müller P, Sell W. A parametric wave prediction model. values are 5.6, 4.9 and 6.5 percent, much smaller than for wind and J Phys Oceanogr 1976;6:200e28. solar. Capacity-down reserves are even lower, 25.3, 26.3 [9] Hasselmann DE, Dunckel M, Ewing JA. Directional wave spectra observed and 31.7 MW for the three types of devices. The ratios to power during JONSWAP 1973. J Phys Oceanogr 1980;10:1264e80. [10] Hasselmann S, Hasselmann K, Allender JH, Barnett TP. Computations and are 5.9, 5.2 and 7.3 percent respectively. parameterizations of the non-linear energy transfer in a gravity wave spec- trum. Part II: parameterizations of the non-linear energy transfer for appli- 7. Conclusions cation in wave models. J Phys Oceanogr 1985;15:1378e91. [11] Janssen PAEM. Quasi-linear theory of wind-wave generation applied to wave e Two conclusions emerge from this analysis. First, geographic forecasting. J Phys Oceanogr 1991;21:1631 42. [12] Janssen PAEM. Progress in ocean wave forecasting. J Comput Phys 2007;227: dispersal of renewable energy generators tends to average out the 3572e94. localized noise, making the power easier to forecast. This is true for [13] Parkinson S, Dragoon K, Reikard G, Ozkan-Haller HT, Brekken TKA. Integrating fi both waves and solar. One further implication of this finding is that ocean wave energy at large scales: a study of the Paci c Northwest. Renew Energy 2015;76:551e9. physics-based wave models may be uniquely well-suited to wave [14] Reikard G. Integrating wave energy into the power grid: simulation and farm simulation. Comparisons of physics model hindcasts with forecasting. Ocean Eng 2013;73:168e78. individual buoy data have generally found that the models produce [15] Retzler C. Measurements of the slow drift dynamics of a model Pelamis wave energy converter. Renew Energy 2006;31:257e69. much smoother values for the wave parameters [53,54]. However, [16] Yemm R, Pizer D, Retzler C, Henderson R. Pelamis: experience from concept to since wave farms will be more dispersed than individual buoys, connection. Philos Trans R Soc 2012;370:365e80. physics model hindcasts can be used to reproduce the wave pa- [17] Henderson R. Design, simulation, and testing of a novel hydraulic power take- off system for the Pelamis wave energy converter. Renew Energy 2006;31: rameters over wider areas. 271e83. Second, wave power remains much easier to forecast than either [18] Pelamis. 2015. www.pelamiswave.com. wind or solar. For wind power, the main issue for the forecaster is [19] Babarit A, Hals J, Muliawan MJ, Kurniawan A, Moan T, Krokstad J. Numerical benchmarking study of a selection of wave energy converters. Renew Energy anticipating the large ramp events. For solar energy, the main 2012;41:44e63. problems are cloud cover and precipitation. While the wave energy [20] Brekken TKA, Ozkan-Haller HT, Simmons A. A methodology for large-scale flux can be extremely volatile, the power output from wave farms is ocean wave power time-series generation. IEEE J Ocean Eng 2012;37: e smoother and more predictable. The main cause is geographic 294 300. [21] Bidlot JR, Holmes DJ, Wittmann PA, Lalbeharry R, Chen HS. Inter-comparison dispersal, but a second factor is that the converters cut off energy of the performance of operational ocean wave forecasting systems with buoy above a given threshold, mitigating the impact of extreme fluctu- data. Weather Forecast 2002;17:287e310. ations. When the costs are expressed in terms of reserves, waves [22] Roulston MS, Ellepola J, von Hardenberg J, Smith LA. Forecasting wave height probabilities with numerical weather prediction models. Ocean Eng 2005;32: are far less expensive than other forms of renewable energy. The 1841e63. findings argue strongly for the development of wave energy at [23] Mathiesen P, Collier C, Kleissl J. A high-resolution, cloud-assimilating nu- coastal locations. merical weather prediction model for solar irradiance forecasting. Sol Energy 2013;92:47e61. [24] Cutler NJ, Outhred HR, MacGill IF, Kay MJ, Kepert JD. Characterizing future Acknowledgments large, rapid changes in aggregated wind power using numerical weather prediction spatial fields. Wind Energy 2009;12:542e55. [25] Cutler NJ, Outhred HR, MacGill IF, Kepert JD. Predicting and presenting The authors thank Frank Vignola of Oregon State University and plausible future scenarios of wind power production from numerical weather Edwin Campos of Argonne National Laboratory for their assistance prediction systems: a qualitative ex ante evaluation for decision making. e in obtaining the solar databases. Wind Energy 2011;15:473 88. 456 G. Reikard et al. / Renewable Energy 81 (2015) 442e456

[26] Reikard G, Pinson P, Bidlot JR. Forecasting ocean wave energy: the ECMWF [40] Paoli C, Voyant C, Muselli M, Nivet ML. Forecasting of preprocessed daily wave model and time series methods. Ocean Eng 2011;38:1089e99. solar radiation time series using neural networks. Sol Energy 2010;84: [27] Pinson P, Reikard G, Bidlot JR. Probabilistic forecasting of the wave energy 2146e60. flux. Appl Energy 2012;93:364e70. [41] Londhe SN, Panchang V. One-day wave forecasts based on artificial neural [28] Marquez R, Coimbra CFM. Forecasting of global and direct solar irradiance networks. J Atmos Ocean Technol 2006;23:1593e603. using stochastic learning methods, ground experiments and the NWS data- [42] Tsai CP, Lin C, Shen JN. Neural network for wave forecasting among multi- base. Sol Energy 2011;85:746e56. stations. Ocean Eng 2002;29:1683e95. [29] Perez R, Kivalov S, Schlemmer J, Hemker K, Renne D, Hoff TE. Validation of [43] Tseng CM, Jan CD, Wang JS, Wang CM. Application of artificial neural net- short and medium term operational solar radiation forecasts in the US. Sol works in typhoon surge forecasting. Ocean Eng 2007;34:1757e68. Energy 2010;84:2161e72. [44] Box GEP, Jenkins GJ. Time series analysis, forecasting and control. San Fran- [30] Pinson P, Nielsen HA, Moller JK, Madsen H, Karinotakis GN. Non-parametric cisco: Holden-Day; 1976. probabilistic forecasts of wind power: required properties and evaluation. [45] Kalman RE. A new approach to linear filtering and prediction problems. Trans Wind Energy 2007;10:497e516. Am Soc Mech Eng J Basic Eng 1960;83D:35e45. [31] Yoder M, Hering AS, Navidi WC, Larson K. Short-term forecasting of cate- [46] Rossi B, Inoue A. Out-of-sample forecast tests robust to the choice of window gorical changes in wind power with Markov chain models. Wind Energy size. J Bus Econ Stat 2012;30:432e53. 2013;17:1425e39. [47] Reikard G. Using temperature and state transitions to forecast wind speed. [32] Bunn DW. Modelling prices in competitive electricity markets. New York: Wind Energy 2008;11:431e43. http://dx.doi.org/10.1002/we/263. Wiley; 2004. [48] Reikard G. Regime-switching models and multiple causal factors in forecasting [33] Granger CWJ. Non-linear models: where do we go next e time varying wind speed. Wind Energy 2010;13:407e18. http://dx.doi.org/10.1002/we.361. parameter models? Stud Nonlinear Dyn Econ 2008;12. Article 1, http://www. [49] Reikard G. Predicting solar radiation at high resolutions: a comparison of time bepress.cxom/snde/vol12/iss3/art1. series forecasts. Sol Energy 2009;83:342e9. http://dx.doi.org/10.1016/ [34] Akaike H. Information theory and the extension of the maximum likelihood j.solener.2008.08.07. principle. In: Petrov BN, Csaki F, editors. Second International Symposium on [50] Huang J, Korolkiewicz M, Agrawal M, Boland J. Forecasting solar radiation on Information Theory. Budapest: Akademiai Kiado; 1973. p. 267e81. an hourly time scale using a coupled autoregressive and dynamic system [35] Cao JJ, Cao SH. Study of forecasting solar irradiance using neural networks with (CARDS) model. Sol Energy 2013;87:136e49. preprocessing sample data by wavelet analysis. Energy 2006;31:3435e45. [51] Zhang GP. Time series forecasting using a hybrid ARIMA and neural network [36] Chen C, Duan S, Cai T, Liu B. Online 24-h solar power forecasting based on model. Neurocomputing 2003;50:159e75. weather type classification using artificial neural network. Sol Energy [52] Order No. 764 Federal Energy Regulatory Center (FERC). Washington, DC: 2011;85:2856e70. Federal Energy Regulatory Center; 2012. [37] Deo MC, Jagdale SS. Prediction of breaking waves with neural networks. [53] Chawla A, Spindler DM, Tolman HL. Validatino of a thirty year wave hindcast Ocean Eng 2003;30:1163e78. using the climate forecast system reananlysis winds. Ocean Model 2012;70: [38] Deo MC, Naidu CS. Real time wave forecasting using neural networks. Ocean 189e206. Eng 1998;26:191e203. [54] Garcia-Medina G, Ozkan-Haller HT, Ruggiero P, Oskamp J. An inner-shelf wave [39] Deo MC, Jha A, Chaphekar AS, Ravikant K. Neural networks for wave fore- forecasting system for the U.S. Pacific Northwest. Weather Forecast 2013;28: casting. Ocean Eng 2001;28:889e98. 681e703.